Hide-and-Seek with the Fundamental Metallicity Relation
aa r X i v : . [ a s t r o - ph . GA ] M a y A CCEPTED FOR PUBLICATION IN THE A STROPHYSICAL J OURNAL L ETTERS
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HIDE-AND-SEEK WITH THE FUNDAMENTAL METALLICITY RELATION
D. K
ASHINO , A. R ENZINI , J. D. S
ILVERMAN , E. D ADDI Accepted for publication in the Astrophysical Journal Letters
ABSTRACTWe use ∼ ,
000 star-forming galaxies at 0 . < z < . II ] λ II ] λλ INTRODUCTION
An anti-correlation of the gas-phase metallicity ( Z ) andstar formation rate (SFR) at a fixed stellar mass ( M ∗ ) hasbeen first reported by Ellison et al. (2008) and then fur-ther explored and discussed in many subsequent studies(e.g., Lara-López et al. 2010, 2013; Mannucci et al. 2011;Yates et al. 2012; Andrews & Martini 2013; Wuyts et al.2014; Zahid et al. 2014). In particular, Mannucci et al. (2010,hereafter M10) proposed the so-called fundamental metallic-ity relation (FMR), as a redshift-invariant surface in the ( M ∗ ,SFR, Z ), with SFR being a third axis in the mass–metallicity(MZ) relation. Such an FMR was then meant to describeboth anti-correlated SFR and Z fluctuations at fixed mass andthe redshift evolution of metallicity and SFR, where, with in-creasing lookback time, the specific SFR (sSFR) goes up and Z goes down, thus keeping galaxies on the FMR.However, large discrepancies still exist concerning the sizeand shape of the SFR - Z anti-correlation in the literature.For example, the anti-correlation is noticeable in M10 atlow masses but nearly vanishes at high masses, whereasin Andrews & Martini (2013) it is nearly equally strong atall masses and much stronger than in M10. On the con-trary, Yates et al. (2012) shows that the metallicity increases,rather than decreases, with increasing SFR for massive galax-ies. Moreover, it is not clear whether an sSFR - Z anti-correlation exists at all at high redshift (e.g., Steidel et al.2014; Wuyts et al. 2014; Zahid et al. 2014; Guo et al. 2016),or whether high redshift galaxies follow the FMR proposedby M10. These discrepancies may largely arise from the useof different metallicity indicators or different galaxy selectioncriteria adopted in different studies.In a physical interpretation of the FMR, upward fluctua-tions in the amount of pristine infalling gas would boost starformation while diluting the metal abundance of the ISM Division of Particle and Astrophysical Science, Graduate School ofScience, Nagoya University, Nagoya, 464-8602, [email protected] INAF Osservatorio Astronomico di Padova, vicolo dell’Osservatorio5, I-35122 Padova, Italy National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI),Todai Institutes for Advanced Study, the University of Tokyo, Kashi-wanoha, Kashiwa, 277-8583, Japan Laboratoire AIM-Paris-Saclay, CEA/DSM-CNRS-Université ParisDiderot, Irfu/CEA-Saclay, Service d’Astrophysique, F-91191 Gif-sur-Yvette, France (Ellison et al. 2008; Mannucci et al. 2010). Lilly et al. (2013)have introduced a physically motivated model that predictsthe metallicity of the ISM as a function of M ∗ and SFR,with infalling and outflowing gas regulating star formationand chemical enrichment in a galaxy (see also Dayal et al.2013). Such an idea has also been suggested from cosmo-logical hydrodynamical simulations (Davé et al. 2012). Thismodel unifies, using a simple relation, both the local up anddown fluctuations of sSFR and metallicity as well as their sec-ular evolution with redshift; see also Maier et al. (2014). Onphysical grounds, one expects an FMR to exist, but observa-tions are still somewhat contradictory as to whether an FMRactually exists, and if so, what is its shape is at low and highredshifts.Recently, a new metallicity calibration has been proposedby Dopita et al. (2016, hereafter D16) that differs substan-tially from previous ones. Oxygen is an α -capture pri-mary element produced by massive stars, whereas nitro-gen has both a primary and secondary component (com-ing from the conversion of carbon and oxygen originallypresent in stars) and is produced both by short- (massive) andlong-leaving (intermediate-mass) stars (e.g., Renzini & Voli1981; Vincenzo et al. 2016). Therefore, the N/O ratio in-creases with increasing metal abundance of the ISM (e.g.,Kewley & Dopita 2002) and with an increasing contributionby intermediate-mass stars, hence, on the specific star forma-tion history of individual galaxies. The novelty of the D16calibration is the use of the line ratio [N II ]/[S II ] as a proxyfor the N/O ratio, where sulfur, like oxygen, is an α -capture primary element. The original FMR, as in M10, was based onthe traditional indicators, the [N II ]/H α and ([O II ] + [O III ])/H β ratios, following the calibration as in Maiolino et al. (2008,hereafter M08).In this paper, we investigate the Z – M ∗ –SFR (i.e., FMR) re-lation while comparing the D16 and M10 calibrations for de-termining the gas-phase metallicity. Throughout this Letter,we use a Chabrier (2003) initial mass function (IMF). SAMPLE
Our galaxy sample is extracted from the Sloan Digital SkySurvey (SDSS) Data Release 7 (Abazajian et al. 2009), whilethe physical quantities of galaxies are based on the MPA-JHU catalog (Kauffmann et al. 2003; Brinchmann et al. 2004;Tremonti et al. 2004) of Data Release 12 (Alam et al. 2015),which provides the total SFRs. SFRs are derived from theH α luminosity, for which dust extinction and fiber aperturelosses are corrected, for star-forming galaxies in our sample(Brinchmann et al. 2004). We use stellar masses derived us-ing Le Phare (Arnouts & Ilbert 2011) and taking into accountthe emission lines in the spectral energy distribution (SED)fitting (see Zahid et al. 2011 for details). SFRs in the MPA-JHU catalog are converted to a Chabrier IMF by subtracting0.05 dex from the original values. We note that M10 usedSFRs measured within the fiber aperture, which are smaller(by roughly one-half) than the total SFRs used in this study.We present here results based on the total (aperture-corrected)SFRs, but we emphasize that the same results and conclusionsare reached when using in-fiber SFRs.Galaxies are selected over a redshift range of 0 . < z < . II ] doublet lines fall within the wave-length range of the SDSS spectrograph (3800–9200 Å). Thelower redshift limit is imposed to reduce the aperture effects.According to Kewley et al. (2005), the line measurements ofgalaxies at z < .
04 tend to be highly biased toward the centralarea, which is typically more enriched, as the covering frac-tion of the SDSS fiber is typically less than ∼ . < z < . Z evolution with redshift.We restrict the sample to galaxies having emission-lines de-tections of H α with S/N > II ] λ II ] λλ β , [O III ] λ II ] λλ > star-forming galaxies from AGNs by applying the simplified formulationderived by Cid Fernandes et al. (2010): N ≡ log (cid:0) [N II ] λ / H α (cid:1) < - . , (1)log (cid:0) [O III ] λ / H β (cid:1) < . N + . + . . (2)Our selection criteria differs from that of M10, who adoptedS/N >
25 for only H α without imposing limits on the otherlines. We have checked that our results and conclusions donot change when using the same criterion adopted in M10. METALLICITY DETERMINATION
For a proper comparison with the result of M10, we furtherimpose a selection based on the method of metallicity deter-mination. For the selected star-forming galaxies, gas-phaseoxygen abundances are estimated using two independent in-dicators, the [N II ]/H α ratio and the R index, defined as R = log ([O II ] λλ , + [O III ] λλ , / H β . Wecorrect the R values for dust extinction based on the Balmerdecrement (H α /H β ) assuming a Calzetti et al. (2000) extinc-tion curve. As in M10, we adopt the M08 calibrations andselect only galaxies in which the two estimates agree within0.25 dex (98% of the sample), for which the metallicity isdefined as an average of the two estimates. Note that our con-clusions do not depend on whether this criterion is applied ornot. The resulting sample consists of 83,076 galaxies.For the same galaxies, the metallicity was determined alsofollowing the D16 calibration using the line ratios [N II ]/[S II ]and [N II ]/H α , which is given to hold over the metallicityrange of 8 < + log(O / H) < + log(O / H) = 8 . + N S + . N N S II ] λ / [S II ] λλ , N II ] λ / H α ). This calibration has the advantage thatit is almost independent of the ionization parameter and gas F IG . 1.— Stellar mass–metallicity relation for our sample of 83,076 galax-ies (0 . < z < .
3) where metallicity is derived from Equation 3. Contoursshow the number distribution of galaxies in log scale. Squares indicate themedian metallicity in bins of stellar mass and the dashed lines indicate thecentral 68th percentile of each bin. pressure (see Figure 2 in D16), as both the [N II ] and [S II ] linesrespond to the changes in the ionization parameter and/or gaspressure in a similar manner, and the wavelength proximity ofthe lines ensures little dependence on reddening.This relation is based on the assumption N/S ≃ N/O and onthe N/O vs. O/H relation derived from local calibrators (Fig-ure 1 in D16), where N/O increases with increasing metallic-ity as the secondary nitrogen production becomes predomi-nant. We also note that variations of the S/O abundance ra-tio are expected to be small ( ∼ . II ]/[S II ] ratio as a proxy for the N/O ratio.However, as mentioned by D16, it remains to be demonstratedwhether the N/O vs. O/H relation implicit in Equation 3 holdsalso at high redshifts. This is to say that the metallicity scalegiven by Equation 3 must hold for the galaxies used to cali-brate it, or having had similar chemical evolutionary histories,and may not apply to galaxies having experienced a differentchemical evolution compared to local calibrators, which maywell include all high redshift galaxies. RESULTS
Figure 1 shows the MZ relation based on the D16 calibra-tion. At M ∗ & M ⊙ , metallicity is strongly correlated withstellar mass, as shown in the MZ relations based on other indi-cators such as the [N II ]/H α ratio (e.g., Zahid et al. 2014). Wefind the scatter σ (log(O / H)) = 0 .
12 dex (8 < log M ∗ / M ⊙ < . ∼ ∼ . M ⊙ ). In such less mas-sive galaxies, the primary nitrogen production may be domi-nant; thus, the secondary-to-primary element ratio (i.e., N/Oand N/S) is almost constant at a value that is determined bythe physics of the primary nucleosynthesis in massive stars( N S ∼ - .
5, e.g., Masters et al. 2014). So, the flattening F IG . 2.— The SFR M ∗ relation color-coded with metallicity derived from the D16 calibration (Equation 3; upper panel) or like in the Mannucci et al. (2010)determination using the N R indices (bottom panel). Contours indicate the number count in cells in log scale. is due to N S - M ∗ relation, color-coded by metal-licity as from the D16 calibration, Equation 3, (upper panel)or based on the M10 determination using N R in-dices (bottom panel). Galaxies are separated in ( M ∗ , SFR)bins with ∆ log M ∗ = 0 . ∆ log SFR = 0 . . . M ∗ / M ⊙ . . In con-trast, the D16 metallicity is nearly invariant with the SFR at afixed stellar mass over the entire stellar mass range probed bythe sample.The disappearance of the SFR dependence of metallic-ity is even more clearly seen in Figure 3, showing the me-dian metallicities with both calibrations as a function of SFRfor galaxies with different masses as labelled. Galaxies arebinned by ∆ log SFR = 0 . ∆ log M ∗ = 0 . N + R -basedmetallicity decreases with increasing SFR. The change inmetallicity tends to be larger for less massive galaxies, while the metallicity is almost invariant with SFR at M ∗ & M ⊙ ,as shown in Figure 2. In contrast, the top panel of Figure 3clearly shows that the D16 metallicity is almost independentof SFR at a fixed stellar mass.Thus, we recover the FMR anti-correlation as in M10when we use metallicities as derived in M10, but the anti-correlation, hence the FMR, apparently disappear when usingthe D16 metallicity scale. So, does the FMR really exist, or isit a mere artifact of a specific metallicity scale?We also notice from Figure 3 (top panel) that metallic-ity increases slightly with increasing SFR in galaxies with M ∗ & M ⊙ . This positive correlation between Z and SFRis statistically significant, while being opposite to the origi-nal FMR. Such an inverse trend at high masses has also beenpointed out also by Yates et al. (2012), and Figure 3 indicatesthat it becomes stronger when using the D16 metallicities,while present also when using the M08 calibration. Clearly,dilution with pristine gas cannot be invoked to account for thistrend. CONCLUSIONS
We measure the metallicity of star-forming galaxies basedon two distinct calibrations: one recently proposed byDopita et al. (2016) incorporating both the [N II ]/[S II ] line ra-tio and N N R indices (as calibrated by Maiolino et al. 2008) us-ing ∼ ,
000 local star-forming galaxies (0 . < z < . Z –SFR anti-correlation at a fixed stellar mass) exists or does not exist de-pending on how metallicity is measured. In particular, theSFR dependence in the MZ relation disappears when using F IG . 3.— Median metallicity computed with either Equation 3 (upper panel)or the M10 calibration (bottom panel), as a function of SFR. Squares indicatemedian metallicities in each ( M ∗ , SFR) cell ( ∆ log M ∗ = 0 . . σ / √ N where σ is a standard deviation and N isthe number of galaxies in each ( M ∗ , SFR) bin. Horizontal dashed lines (toppanel) indicate the median metallicities measured in each stellar mass bin. the D16 metallicity, while we retrieve it when using the samemetallicity scale adopted by M10.However, ironically enough, we maintain that the disap-pearance of the FMR with D16 is actually consistent with itsexistence. Indeed, if enhancement of star formation and di-lution of gas-phase oxygen abundance are both driven by in-fall of pristine/metal-poor gas, one does not expect the N/Sand N/O ratios to change at all. Now, in Equation 3, theoxygen abundance depends linearly on the [N II ]/[S II ] ratio(which does not change by dilution) and only to the ∼ / II ]/H α ratio, whereas both ratios span a sim-ilar range ( ∼ II ]/[S II ] ratio, the D16 metallicity is almost insensitive todilution effects that may be present in low as well as high red-shift galaxies. In essence, the D16 metallicity scale cannotbe used to uncover an FMR if it really exists, but the lack ofan SFR - Z